There are actually two menus behind the scenes, though they are intended to look the same. The first one was designed to only tease you with options during the first playthrough and wasn't designed with NG+ in mind. Those options are not genuine, and it would take some effort to get them to work properly.
My current plan is to get rid of that first menu entirely, removing any confusion stemming from it. You are supposed to climb with Nell twice before you get to do any naughty stuff with her, and that will continue to be true in the future, even for NG+.